The DNA topoisomerase IB (ToplB) family includes the eukaryotic nuclear and mitochondrial ToplB enzymes, the poxvirus topoisomerases, mimivirus ToplB, and the poxvirus-like topoisomerases of bacteria. ToplB enzymes relax DNA supercoils by iteratively breaking and rejoining one strand of the DNA duplex through a covalent DNA-(3'-phosphotyrosyl)-enzyme intermediate. Vaccinia ToplB, which displays stringent specificity for cleavage at the sequence 5'(C/T)CCTT], in the scissile strand, provides a highly instructive model system for mechanistic studies of the ToplB family. Its cleavage and religation transesterification reactions are driven by a constellation of four amino acid side chains (Arg130, Lys167, Arg223, His265) that catalyzes the attack of Tyr274 on the scissile phosphate to form the covalent intermediate and expel a 5'-0H leaving strand. The active site is not preassembled in the apoenzyme; rather its assembly is triggered by recognition of the CCCTT target site. Our functional studies of ToplB mutants and DNA target modifications are contributing to a coherent model of the ToplB mechanism, and the likely steps in active site recruitment. We aim to dissect in a comprehensive fashion the contributions of individual atomic contacts between the vaccinia ToplB and the DNA during active site assembly, transesterification, and supercoil relaxation. Our studies of DNA transesterification have inspired us to investigate site-specific and end-specific transesterification reactions of RNA and the enzymes that catalyze them. This is an emerging field of study that embraces many important biological phenomena, including host antiviral defense, RNA-based innate immunity, cellular stress responses, and tRNA splicing.